The most widely used method for simulating the non-linear behaviour of concrete and masonry structures is the Newton–Raphson method with arc-length control (N-R method). However, this method may fail to produce converged results because of softening, negative tangent stiffness, bifurcations or snap-back. Sometimes, convergence can be obtained by controlling degrees of freedom in the failure process zone or by applying sequentially linear analysis (SLA). However, the location of the failure is often not known a priori and geometrical non-linearity needs to be included. Recently, incremental sequentially linear analysis (ISLA) has been proposed, which is based on a combination of the N-R method and SLA. The solution search path follows damage cycles sequentially with secant stiffness corresponding to local damage increments, which traces both damage history (explicit) and displacement history (implicit). The objective of this paper is to demonstrate that ISLA can be applied to problems that behave geometrically nonlinear in addition to physically nonlinear. In this paper, we introduce a method that combines ISLA with indirect displacement control. This method stabilises localised damage process areas and avoids the global unloading caused by geometrical and physical non-linearity. The method uses one or more control points, which are positioned independently of the failure process zones. Two masonry walls were tested and analysed. The load was perpendicular to their planes and evenly distributed. The walls were supported on two or four edges. Stable post-peak results were computed for large geometrical non-linear displacements, and localised crack propagation was computed robustly and correctly.

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In the past decades, great progress has been made in analyzing lateral torsional buckling of slender beams. The phenomena has been accurately described by differential equations, closed form solutions are available for specific cases and the solution for any load and any boundary condition can be obtained by finite element analysis. Timber and steel design standards provide a procedure based on equivalent moment factors. With this procedure, beams can be designed straightforwardly. However, modern designers continue to push the envelope and more irregular load patterns are found, on which the design standards do not provide solutions. Consequently, designers are forced to determine the equivalent moment factors based on case-specific literature and/or conservative assumptions. Unfortunately, this makes many challenging modern designs uneconomical. Furthermore, significant inconsistencies between the different design procedures are found. For that purpose, this paper proposes a solution in the form of a general formulation to determine equivalent moment factors for any loading on a single-span beam for both free and restrained lateral bending and/or warping at the supports, for both I-sections and rectangular slender sections loaded in the shear center. It is shown that the obtained moment factors are accurate and in good agreement with design standards and literature, and a wide range of irregular load patterns is considered.

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Incremental Sequentially Linear Analysis (ISLA) is a new algorithm for non-linear finite element analysis. It is an extension of Sequentially Linear Analysis (SLA) which has been applied since 2001 as an alternative to the Newton-Raphson method when bifurcation, snap-back or divergence problems arise. ISLA is an incremental procedure with an implicit scheme, which starts and ends with an equilibrium state. The solution search path fol-lows damage steps sequentially with secant stiffness. In each iteration only one element is selected for damaging in the next iteration, which is a similar procedure as used in SLA. In this paper, ISLA is explained and demonstrated for a notched beam test. Because of the incremental procedure, ISLA can be extended to non-proportional loading, geometrically non-linear analysis and transient analysis. The searching path of ISLA is based on physical parameters (damage and history) rather than guided by numerical parameters. In addition, the method keeps the same incremental format throughout the entire analysis, circumventing the need to switch intermittently from incremental to total approaches or vice versa.@en

Quasi brittle materials, such as un-reinforced masonry or concrete are difficult to analyse because often the traditional Newton–Raphson (N-R) procedure fails to converge. Many solutions have been proposed such as Sequentially Linear Analysis (SLA), but these may fail in case of non-proportional loading with a large prestress. In this paper a new method is proposed that is based on a combination of the Newton–Raphson method and Sequentially Linear Analysis. The method is incremental; each increment starts and ends with an equilibrium state. The solution search path follows damage cycles sequentially with secant stiffness. The proposed method is demonstrated to be robust and accurate. It has been tested on prestressed concrete beams. It can be naturally extended to other types of analyses (e.g. geometrically non-linear analysis and transient analysis) due to the incremental procedure. In addition, it is shown that high prestress values can transform the behaviour of a concrete beam from softening to hardening.@en

Double-curved structures in general, and monolithic concrete shell structures more specifically, can transfer forces very efficiently. As a result, the thickness-to-span ratio can be very low, which, material-wise, can lead to a very economical design. However, the construction of shell structures is very labour-intensive and comes with high formwork costs and shells in modern building practice are rarely constructed. Concrete shell structures can be cast in-situ making use of temporary formwork and falsework, but they can be (partially) prefabricated as well, like the Palazzetto dello Sport in Rome. Although precasting is an effective technology for the repetitive production of concrete elements, for double-curved structures, having a large variety of shapes, the advantages of precasting seem to diminish quickly as a result of high formwork costs. Another disadvantage of precasting shell elements obviously seems to be the complexity of the required connections. For shell structures, the loss of stiffness of the connections might even lead to a crucial reduction of the buckling stability. A combination of both building methods, the prefabrication of the supportive structure and a finish with a cast in-situ layer, solves this before-mentioned issues and the advantages of both methods are combined: reduction of the complexity of the connections with an in-situ cast concrete layer and integration of the supportive structure in the design for a more cost-efficient erection. This paper describes the study of an innovative, partially precast, alternative solution for the construction of shell structures, and specifically addresses the influence of connections between precast elements on the overall shell behaviour. The Green Planet gas station along the A32 highway in The Netherlands was selected as a design case for such a building method.@en

The problem minimizing the number of specimens required for fatigue data analysis is considered in this research. Assuming unknown hyperparameters described via prior distributions, a hierarchical Bayesian model with accumulated prior information was proposed to deal with this issue. One of the main advantages of hierarchical Bayesian model over the empirical Bayesian model is that the prior distributions with hierarchical structure can incorporate structural prior and subjective prior simultaneously. The probabilistic stress-cycle (P-S-N) curves are generated from the predictive distributions, involving both the randomness of parameters and the scatter of observations, and calculated by an identical hierarchical structure. The numerical calculation is done via the Gibbs sampler, which makes the whole process simple and intuitive.

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The precise geometries of three reinforced concrete shell roofs have been measured with a laser scanner. The resulting point cloud has been modelled by NURBS surfaces. Two methods have been developed for determining the shape imperfections with lengths between 0.5 and 5.5 m. The largest observed imperfection amplitude is 80 mm with length of 5 m. The imperfections are represented by a variance spectrum and an extreme value distribution. From this are derived a formula for the characteristic imperfection amplitude and the partial safety factor.@en

Sequentially linear analysis (SLA) is an alternative to the Newton-Raphson method for analyzing the nonlinear behavior of reinforced concrete and masonry structures. In this paper SLA is extended to load cases that are applied one after the other, for example first dead load and then wind load. It is shown that every nonlinear analysis step can be made in just two linear elastic analysis steps. The proposed algorithm is extremely robust, which is demonstrated in a prestressed concrete beam analysis. A comparison is made between results of SLA and Newton-Raphson with arch length control.@en